$\dfrac{ 4x - 10y }{ 7 } = \dfrac{ -9x - 7z }{ 8 }$ Solve for $x$.
Solution: Multiply both sides by the left denominator. $\dfrac{ 4x - 10y }{ {7} } = \dfrac{ -9x - 7z }{ 8 }$ ${7} \cdot \dfrac{ 4x - 10y }{ {7} } = {7} \cdot \dfrac{ -9x - 7z }{ 8 }$ $4x - 10y = {7} \cdot \dfrac { -9x - 7z }{ 8 }$ Multiply both sides by the right denominator. $4x - 10y = 7 \cdot \dfrac{ -9x - 7z }{ {8} }$ ${8} \cdot \left( 4x - 10y \right) = {8} \cdot 7 \cdot \dfrac{ -9x - 7z }{ {8} }$ ${8} \cdot \left( 4x - 10y \right) = 7 \cdot \left( -9x - 7z \right)$ Distribute both sides ${8} \cdot \left( 4x - 10y \right) = {7} \cdot \left( -9x - 7z \right)$ ${32}x - {80}y = -{63}x - {49}z$ Combine $x$ terms on the left. ${32x} - 80y = -{63x} - 49z$ ${95x} - 80y = -49z$ Move the $y$ term to the right. $95x - {80y} = -49z$ $95x = -49z + {80y}$ Isolate $x$ by dividing both sides by its coefficient. ${95}x = -49z + 80y$ $x = \dfrac{ -49z + 80y }{ {95} }$